President Trump criticized James Dimon on Thursday as a “poor public speaker” and “nervous mess,” a day after the JPMorgan Chase & Co. chief executive said he could prevail over Mr. Trump in a presidential campaign.

“The problem with banker Jamie Dimon running for President is that he doesn’t have the aptitude or “smarts” & is a poor public speaker & nervous mess - otherwise he is wonderful,” Mr. Trump tweeted. “I’ve made a lot of bankers, and others, look much smarter than they are with my great economic policy!"

At a bank event Wednesday, Mr. Dimon said he thought he could defeat Mr. Trump but couldn’t “beat the liberal side of the Democratic Party.” He also took shots at the president’s intelligence and wealth, calling himself “as tough as [Trump] is” but “smarter than he is.” Mr. Dimon added: “This wealthy New Yorker actually earned his money. It wasn’t a gift from Daddy.”

After the event concluded, Mr. Dimon backtracked. “I should not have said it. I’m not running for President. Proves I wouldn’t make a good politician. I get frustrated because I want all sides to come together to help solve big problems,” he said in an emailed statement through a JPMorgan spokesman.

A JPMorgan spokesman declined to comment on Mr. Trump’s tweet.

Mr. Dimon served on the president’s business advisory council until it disbanded in August 2017. His political ambitions are the subject of frequent speculation, especially on Wall Street. In the past, Mr. Dimon said he’d “love to have the job, but I’m not going to run.”

Mr. Trump’s tweet came as the federal government is working to prepare for Hurricane Florence to make landfall on the East Coast. His campaign canceled rallies with Mr. Trump on Thursday and Friday due to the impending storm. Less than 20 minutes after his tweet to Mr. Dimon, Mr. Trump warned that the storm was growing “even larger.”